The unnamed suspect, who also injured himself, was arrested shortly after the attack in Saarbrücken, near the French border, and was then hospitalized, police said.
The victim was a psychologist who worked with traumatized refugees, said the German Red Cross.
According to police, the suspect had gotten into an argument during a counselling session with the 30-year-old psychologist and stabbed him with a knife. The psychologist died of his injuries at the therapy centre. The reason for the conflict is still unclear, but police said they had ruled out terrorism.
Die Welt reported that the psychologist had himself immigrated to Germany, moving to the country from Iraq in 2005. The victim, Musaab al-T., completed his bachelor's degree in psychology in Saarbrücken and was finishing his master's degree.
"I was born and raised in war," he had told the Saarbrücker Zeitung last year.
German Red Cross president Rudolf Seiters said he was "appalled and shocked" by the crime.
"All of the German Red Cross mourns the admirable worker," Seiters added. "Our sympathy is with the family members."
A spokesman from the Red Cross said that there is always a risk in working with people coming from war-torn countries. The state Red Cross in Saarland has about 2,500 full-time employees, and more than 6,000 volunteers.